Let `veca vecb and vecc` be pairwise mutually perpendicular vectors, such that `|veca|=1, |vecb|=2, |vecc| = 2`, the find the length of ` veca +vecb + vecc`.

Explanation

To find the length of the vector sum \(\vec{a} + \vec{b} + \vec{c}\), where \(\vec{a}\), \(\vec{b}\), and \(\vec{c}\) are pairwise mutually perpendicular vectors with magnitudes \(|\vec{a}| = 1\), \(|\vec{b}| = 2\), and \(|\vec{c}| = 2\), we can follow these steps:

### Step 1: Understand the properties of mutually perpendicular vectors
Since the vectors are mutually perpendicular, the dot product between any two different vectors is zero. This means:
\[ \vec{a} \cdot \vec{b} = 0, \quad \vec{b} \cdot \vec{c} = 0, \quad \vec{c} \cdot \vec{a} = 0 \]

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